The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^3+X  1 X^2  1 X^2+X X^2 X^3+X^2+X X^3+X^2+X  0 X^3  1  1 X^2  1  1  1 X^2  1  1  1  1  1 X^3+X^2 X^3+X  1  1  1  0  1  1  1 X^3 X^3+X^2+X X^2 X^3+X^2+X  0  1  1  1 X^3+X^2+X  1  1 X^2 X^3+X X^2  1 X^2+X  1 X^3  1  1  1  1 X^3+X^2  1  X X^3+X^2+X X^3+X^2  1  1  1 X^3+X  1  1  1 X^3+X^2+X  1  1  1
 0  1  0  0  0 X^3+X^2+1 X^3+X+1  1 X^3+1 X+1 X^3 X^3+X  1 X^3+X^2  1 X^3+X^2  1 X^2+X  1 X^2 X^3+X X+1  1 X^3+1 X^2+1  0  1 X^2+X X+1 X^2+X X^3+X^2+X X^2+X  1  1 X^2 X^3+X^2+X+1 X^3+X  X X^3+1 X^3+X+1 X^3 X^3+X^2+X X^2  1  X  1 X^3+1 X^2+1 X^3+X^2  1 X^3+X+1 X^3+X^2 X^3+X^2 X^3+X  1 X^3+X^2+X  1 X^3+1  1 X^3+X^2+X X^2 X+1  1  1  1  0 X^2+X  1 X^3+X+1 X^2+1 X^2+1  1 X^3+X^2+X+1  0  0  1 X^2 X^3+X+1 X^3
 0  0  1  0 X^2 X^3 X^3+X^2  0 X^3+1 X^3+X^2+X+1  1 X^3+1 X^2+1 X^2+1 X+1 X^3+X X^2+X  1 X+1  1 X^2 X^3+X X^3+X^2 X+1 X^3+X^2+1 X^3+X^2+X X+1  1  X X^3+X^2+X+1 X^3+X^2+1 X^3+X X^3+X^2+X X^2+1 X^3+X+1 X^3 X^3 X^3+X X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1  1  1  1  1 X^3 X+1 X^3+X^2+X X^3+X X^3+X^2+1 X^3+X^2+X  0  1  X  1 X^3+X X^2+X+1 X^2  1 X^3 X^3+X X^3  0  1 X+1 X^2  1  0 X^3+X^2 X^2+X+1 X^2+X X^3+X^2+X+1 X^2+X+1  1 X+1 X^3+X^2 X^3+1  X  0
 0  0  0  1 X^2+X+1 X^3+X^2+X+1 X^3  1 X^3 X^3+X^2+X+1 X^3+1 X^2 X^3+X^2+X+1 X^3+X+1 X^2  1 X^3+1 X^3+X^2+1  1  X  0  0 X^2+X X^3+X^2+X+1 X^2+X X^3+X+1 X^2+X  1 X^2+X+1 X^3+X X^3+X+1 X^2  X X^3  X X^2+X+1 X^3+1  1 X^2 X^3+X^2+X X^3+X X^3+X X^3+X^2+X+1 X^2+1 X^3 X^3+X X^2+1 X^3+X^2+X+1 X^3+X^2 X^2+X+1 X^3 X^3+X^2+X X^3+X^2+1  1  1 X^3+X^2+1 X^3+X  0 X^2 X^3+X^2+X+1  X X^3+X X^2+1 X^3+X^2+X+1  X  1 X^2+1 X^3+1  X  1  X X^3+X^2 X^2+X X^3 X^3+X^2+1  1 X^2+X  X  X
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+258x^71+1537x^72+3348x^73+5152x^74+8120x^75+10444x^76+12862x^77+15558x^78+16584x^79+15536x^80+13490x^81+10710x^82+7716x^83+4782x^84+2602x^85+1162x^86+668x^87+337x^88+108x^89+34x^90+24x^91+18x^92+4x^93+8x^94+6x^95+1x^96+2x^97

The gray image is a linear code over GF(2) with n=632, k=17 and d=284.
This code was found by Heurico 1.16 in 182 seconds.